Probability density estimation from data is a widely studied problem. Often, the primary goal is to faithfully mimic the underlying empirical density. Having an interpretable model that allows insight into why certain predictions were made is often of secondary importance. Using logic-based formalisms, such as Markov logic, can help with interpretability, but even in Markov logic it can be diff...

-Possibilistic logic and Bayesian networks have provided advantageous methodologies and techniques for computerbased knowledge representation. This paper proposes a framework that combines these two disciplines to exploit their own advantages in uncertain and imprecise knowledge representation problems. The framework proposed is a possibilistic logic based one in which Bayesian nodes and their ...

We investigate the following extendability problem for systems, for which the available information is given by a monotone set mapping M on the field CT of measurable cylinders of a product ample space (XT ,RT ): given that M is invariant under a RT −RT measurable transformation H of XT , i.e. M(H−1(B)) = M(B) for all B ∈ CT , is it possible to find H-invariant monotone extensions of M to the p...

The conventional wisdom is that the concept of information is closely related to the concept of probability. In Shannon's information theory, information is equated to a reduction in entropy—a probabilistic concept. In this paper, a different view of information is put on the table. Information is equated to restriction. More concretely, a restriction is a limitation on the values which a varia...

In this paper, we propose a modified version of the Näıve Possibilistic Classifier (NPC) which has been already suggested to make decision from numerical data. As the former NPC, the modified classifier makes use of the probability to possibility transformation of Dubois et al. in the continuous case in order to estimate possibilistic beliefs. However, unlike the former NPC which uses the produ...

Graphical belief models are compact and powerful tools for representing and reasoning under uncertainty. Possibilistic networks are graphical belief models based on possibility theory. In this paper, we address reasoning under uncertain inputs in both quantitative and qualitative possibilistic networks. More precisely, we first provide possibilistic counterparts of Pearl’s methods of virtual ev...

We explore an approach to possibilistic fuzzy clustering that avoids a severe drawback of the conventional approach, namely that the objective function is truly minimized only if all cluster centers are identical. Our approach is based on the idea that this undesired property can be avoided if we introduce a mutual repulsion of the clusters, so that they are forced away from each other. We deve...

In 2004 Fullér and Majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact. Based on this approach, in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to t...

This article discusses the basic features of information provided in terms of possibilistic uncertainty. It points out the entailment principle, a tool that allows one to infer less specific from a given piece of information. The problem of fusing multiple pieces of possibilistic information is and the basic features of probabilistic information are described. The authors detail a procedure for...